machine_learning.dimensionality_reduction
=========================================

.. py:module:: machine_learning.dimensionality_reduction

.. autoapi-nested-parse::

   Requirements:
     - numpy version 1.21
     - scipy version 1.3.3
   Notes:
     - Each column of the features matrix corresponds to a class item



Functions
---------

.. autoapisummary::

   machine_learning.dimensionality_reduction.column_reshape
   machine_learning.dimensionality_reduction.covariance_between_classes
   machine_learning.dimensionality_reduction.covariance_within_classes
   machine_learning.dimensionality_reduction.linear_discriminant_analysis
   machine_learning.dimensionality_reduction.principal_component_analysis
   machine_learning.dimensionality_reduction.test_linear_discriminant_analysis
   machine_learning.dimensionality_reduction.test_principal_component_analysis


Module Contents
---------------

.. py:function:: column_reshape(input_array: numpy.ndarray) -> numpy.ndarray

   Function to reshape a row Numpy array into a column Numpy array
   >>> input_array = np.array([1, 2, 3])
   >>> column_reshape(input_array)
   array([[1],
          [2],
          [3]])


.. py:function:: covariance_between_classes(features: numpy.ndarray, labels: numpy.ndarray, classes: int) -> numpy.ndarray

   Function to compute the covariance matrix between multiple classes
   >>> features = np.array([[9, 2, 3], [4, 3, 6], [1, 8, 9]])
   >>> labels = np.array([0, 1, 0])
   >>> covariance_between_classes(features, labels, 2)
   array([[ 3.55555556,  1.77777778, -2.66666667],
          [ 1.77777778,  0.88888889, -1.33333333],
          [-2.66666667, -1.33333333,  2.        ]])


.. py:function:: covariance_within_classes(features: numpy.ndarray, labels: numpy.ndarray, classes: int) -> numpy.ndarray

   Function to compute the covariance matrix inside each class.
   >>> features = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
   >>> labels = np.array([0, 1, 0])
   >>> covariance_within_classes(features, labels, 2)
   array([[0.66666667, 0.66666667, 0.66666667],
          [0.66666667, 0.66666667, 0.66666667],
          [0.66666667, 0.66666667, 0.66666667]])


.. py:function:: linear_discriminant_analysis(features: numpy.ndarray, labels: numpy.ndarray, classes: int, dimensions: int) -> numpy.ndarray

   Linear Discriminant Analysis.

   For more details, see: https://en.wikipedia.org/wiki/Linear_discriminant_analysis.
   Parameters:
       * features: the features extracted from the dataset
       * labels: the class labels of the features
       * classes: the number of classes present in the dataset
       * dimensions: to filter the projected data for the desired dimension

   >>> test_linear_discriminant_analysis()


.. py:function:: principal_component_analysis(features: numpy.ndarray, dimensions: int) -> numpy.ndarray

   Principal Component Analysis.

   For more details, see: https://en.wikipedia.org/wiki/Principal_component_analysis.
   Parameters:
       * features: the features extracted from the dataset
       * dimensions: to filter the projected data for the desired dimension

   >>> test_principal_component_analysis()


.. py:function:: test_linear_discriminant_analysis() -> None

.. py:function:: test_principal_component_analysis() -> None